Wavelets — something for analytical chemistry?

Abstract Wavelets have shown great applicability in many diverse fields of science, and are now becoming of interest in analytical chemistry. This paper is intended as a first reading, introducing fundamentals of wavelets and wavelet transforms, and some applications thereof, such as signal compression and denoising, image processing, data set compression and the modeling of multivariate data sets.

[1]  M. Bos,et al.  The wavelet transform for pre-processing IR spectra in the identification of mono- and di-substituted benzenes , 1994 .

[2]  Bruce R. Johnson,et al.  Wavelet based in eigenvalue problems in quantum mechanics , 1996 .

[3]  M. Bos,et al.  Wavelet transform for the evaluation of peak intensities in flow-injection analysis , 1992 .

[4]  I. Daubechies.  Orthonormal bases of compactly supported wavelets , 1988 .

[5]  Yves Meyer,et al.  Progress in wavelet analysis and applications , 1993 .

[6]  M. Grasserbauer,et al.  Wavelet denoising of Gaussian peaks: A comparative study , 1996 .

[7]  D. Massart,et al.  Application of Wavelet Packet Transform in Pattern Recognition of Near-IR Data , 1996 .

[8]  Desire L. Massart,et al.  Noise suppression and signal compression using the wavelet packet transform , 1997 .

[9]  Desire L. Massart,et al.  Standardization of near-infrared spectra in the wavelet domain , 1997 .

[10]  Bhavik R. Bakshi,et al.  Reasoning in Time: Modeling, Analysis, and Pattern Recognition of Temporal Process Trends , 1995 .

[11]  Stéphane Mallat,et al.  A Theory for Multiresolution Signal Decomposition: The Wavelet Representation , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[12]  Desire L. Massart,et al.  Wavelet packet transform applied to a set of signals: A new approach to the best-basis selection , 1997 .

[13]  M. Victor Wickerhauser,et al.  Adapted wavelet analysis from theory to software , 1994 .

[14]  I. Johnstone,et al.  Wavelet Threshold Estimators for Data with Correlated Noise , 1997 .

[15]  Dennis Gabor,et al.  Theory of communication , 1946 .

[16]  Jean-Louis Calais,et al.  Wavelets - Something for quantum chemistry? , 1996 .

[17]  Ronald A. DeVore,et al.  Image compression through wavelet transform coding , 1992, IEEE Trans. Inf. Theory.

[18]  Bhavik R. Bakshi,et al.  Representation of process trends—III. Multiscale extraction of trends from process data , 1994 .

[19]  R. Coifman,et al.  Fast wavelet transforms and numerical algorithms I , 1991 .

[20]  Junbin Gao,et al.  Application of the Fast Wavelet Transform Method to Compress Ultraviolet-Visible Spectra , 1996 .

[21]  Wei,et al.  Wavelets in self-consistent electronic structure calculations. , 1996, Physical review letters.

[22]  G. MallatS..  A Theory for Multiresolution Signal Decomposition , 1989 .

[23]  Ronald R. Coifman,et al.  Entropy-based algorithms for best basis selection , 1992, IEEE Trans. Inf. Theory.

[24]  Sg Nikolov,et al.  DE-NOISING OF SIMS IMAGES VIA WAVELET SHRINKAGE , 1996 .

[25]  Truong Q. Nguyen,et al.  Wavelets and filter banks , 1996 .

[26]  D. Kell,et al.  An introduction to wavelet transforms for chemometricians: A time-frequency approach , 1997 .

[27]  D. Donoho.  Wavelet Shrinkage and W.V.D.: A 10-minute tour , 1997 .

[28]  D. Massart,et al.  Application of wavelet transform to extract the relevant component from spectral data for multivariate calibration. , 1997, Analytical chemistry.